BBS Business Statistics

What is chronological classification? Give an example.

State any two principle objectives of classification.

Construct a frequency table for the following data regarding annual profit, in lakhs of rupees in 50 firms taking 25 - 34, 35 - 44 etc. as class intervals.

i. Find the number of firms having profit between Rs. 37 lakhs and Rs. 58 lakhs.

 ii. Profit above which 10% of the firm will have their profits.

 iii. Middle 50% profit group.

Define the qualitative classification of data with a suitable example.

Find the combined mean of the following data : 

  Before and after the implementation of an economic program to uplift the economic condition of a community following information were found.

a. Find the highest income of the poorest 40% of the population before and after the plan.

b. Find the lowest income of richest 40% of the population before and after the plan.

c. Obtain the limits of income of middle 50% of families before and after the plan.

The following table shows the monthly income of workers of two manufacturing companies A and B

The following table shows the monthly  income of 

workers of two manufacturing Companines A and B 

                                          Company A Company B 

Mean -monthly income Rs 2550       Rs .2800 

Numbers of workers           100       110 

An enquiry into the budget of middle class families in a certain locality of a city gave the following information:

What is the cost of living index number of 2022 as compared to 2021? If an Employee's monthly salary is Rs. 40,500 in base period what should be his/her salary in current period ? 

The following table shows the average daily wages of workers in city A and B, find the combined average wage of the workers.

The following table shows the marks distribution of students of a college:

Calculate limits of marks obtained by middle 80% of the students.

Coefficient of variation of a distribution is found to be 20% and variance of distribution is 36. Find the mean value of the distribution.

Following two groups of samples describes the age of the students in regular morning MBS program and evening MBS program of National College. If homogeneity of the class is a positive factor for learning which of the two programs will be easier to teach.

A factory produces two types of electric lamps A and B. In an experiment relating to their life, the following results were obtained:

(a) Find which model of electrical lamp has greater uniformatily of life ? Give the reason 

(b) Calculate the combined standard deviation 

If the third quartile and median are 30 and 22 respectively. Find the first quartile, assuming the distribution to be symmetrical.

Calculate the coefficient of variation of a distribution, if mean is found to be 200 and variance of distribution is 36.

Find the coefficient of quartile deviation of a distribution when upper and lower quartiles are 90 and 55 respectively.

Find the appropriate measure of dispersion from the following income table:

Following two samples describes the age (year) of the students in regular MLS programme of a University:

(a) If homogeneity of the age is a positive factor for teaching-learning process, which of the two programmes will be easier to teach?
(b) Calculate combined standard deviation.

Find the Karl Pearson's Coefficient of Skewness, when mean = 45, mode = 48 and standard deviation = 15.

The quartile deviation of a distribution is 2 and the difference between P9 and P10 is 8. Calculate the coefficient of Kurtosis.

 Calculate the karl Pearson's Coefficient of skewness and interpret the result . 

Test for the normality of these two distributions of wages (in Rs.) and interpret the result on the basis of the information given below:

If mean = 35, mode = 40 and standard deviation = 10. Find Karl Pearson's coefficient of skewness and interpret the result.

The standard deviation of mesokurtic distribution is 7. What must be the value of fourth moment about mean?

The following data shows the income distribution of families of a certain locality of a city. Calculate the coefficient of skewness and kurtosis and hence comment on the nature of the income distribution.

If mean = 25, mode = 28 and standard deviation = 5, find coefficient of skewness.

If the quartiles coefficient of skewness is 0.6, quartile deviation is 5 and the third quartile is 28, find the median of the distribution.

Calculate percentile coefficient of kurtosis for the following data:

The Karl Pearson's coefficient of skewness is 0.5 if mean = 45 and standard deviation = 15, find the value of mode.

The following table shows the distributions of wages (in Rs) of workers. Test the normality of the wage distribution.

Calculate coefficient of correlation between X and Y if the regression coefficient of Y on X is -0.667 and regression coefficient of X on Y is -0.75.

The income and expenditure of 100 families is given below:

 Find (a) Two regression co-effcient . 

(b) Co -efficient of correlation between income and expenditure . 

(c) Estimate the expenditure when income is Rs 10,000.      

Find Karl Pearson's correlation coefficient between X and Y from the following information. N = 10, ΣX = 125, ΣY = 50, ΣX² = 2080, ΣY² = 2085, ΣXY = 1050

The following two way table shows the sales revenue (in lakhs Rs.) and advertising expenditure (in lakhs Rs.) of a company. Find correlation coefficient between them and interpret the result. Also test the significance of correlation coefficient. Estimate the sales revenue when advertising expenditure is Rs. 50 lakhs

Given the following Regression equations,

(i) The coefficient of rank correlation of marks obtained by 10 students, in Statistics and Account was found to be 0.5. It was later discovered that the difference in ranks in the two subjects obtained by one student was wrongly taken as 3 instead of 7. Find the correct coefficient of rank correlation.

(ii) An analysis of the monthly wages paid to workers in the firm A and B belonging to the same industry given the following results.

(a) Which firm pays larger wage bill?**
(b) In which firm is there greater variability in individual wages?**

The following table gives information on ages and cholesterol levels for a random sample of 10 men. Develop the regression line of cholesterol level on age.

Predict the cholesterol level of a 60 - year -old man.

Calculate coefficient of correlation (r), if byx = -0.57 and bxy = -0.82 respectively.

The following table provides the fertilizer used and production of paddy in certain plots of hilly region of Nepal.

a) Find two regression co-efficients.
b) Calculate the co-efficient of correlation between fertilizer used and production of paddy and interpret the result.
c) Estimate the production of paddy when fertilizer used is 50 metric tons.

What are the components of a time series.

The year of origin of the following trend line equation of sales (in millions rupees) is 2015. Y = 50 + 2.5X Estimate the sales for the year 2022.

The following table reveals the sales distribution of a business house from the year 2016 to 2020:

 Filt a trend line equation of given data . Calculate trend values and estimates sales of the year 2024. 

The year of origin of the following trend line equation of production (in tonne's) is 2017. \( y = 40 + 1.5x \). Estimate the production for the year 2033.

Below are given the annual production of sugar (in thousand tons) of a factory

i. Fit a straight by the method of least square

ii. Obtain the trend values

 iii. Plot the given figures on a graph and show the trend line

iv. What is the monthly increase in production?

v. Estimate production of sugar for the year 2020.

The following time series data shows the profit (million Rs) of XYZ company from the fiscal year 2015 to 2023:

a. Fit a straight line trend to these data.

b. Calculate the trend values and short term fluctuations.

c. Plot the actual data as well as the trend values on graph paper.

d. Estimate the profit for 2024.

e. What is the monthly increment of the profit?

 Find the simple aggregative price index number for the year 2021 : 

The following table gives the changes in the price and the consumption (quantity) of certain major constituents of the consumption basket of the labor class.

Find simple aggregative price index number for the year 2021 from the following information.

Find the simple aggregative price index number from the following data of 2015 taking 2014 as base year when current year quantity is taken as weight.

An inquiry into the budget of middle class families in a certain city gave the following information

What is the cost of living index number of 2016 as compared with that 2015. If an employee's salary of Rs. 20,000 per month is raised to Rs. 21,000 in 2016, is it adequate? If not, what should be the increment in salary in 2016?

Find the simple aggregative price index number from the following data:

The following table gives the changes in the price (in Rs) and the quantity (units) of certain commodities:

Calculate price index number according to
(a) Laspeyre's formula
(b) Paasche's formula
(c) Fisher's ideal formula.

(a) Solve the following Linear Programming problem graphically:
Maximize Z = 4x + 3y
Subject to constraints: 2x + y ≤ 10
x + y ≤ 6

and x ≥ 0, y ≥ 0

(b) The following table is the conditional payoff table   

Provide a decision according to:
i) Maximax criterion
ii) Maximin criterion
iii) Minimax regret criterion

If P(A) = 0.6, P(B) = 0.56 and P(A∪B) = 0.75 find P(A∩B). Where A and B are not disjoint events.

(a) The probability that a boy will get a scholarship is 0.9 and that a girl will get is 0.8. What is the probability that at least one of them will get the scholarship? (b) The following table is the conditional payoff table:

 What will be your decision if : (i) Maximum criterion is used (ii) Maximum Criterion is used (iii) Minimax regret criterion is used 

Ram and Sita appear for an interview for two different posts. The probabilities of their selection are 3/4 and 1/5 respectively. Find the probability that (a) both of them will be selected (b) none of them will be selected.

A card is drawn at random from a pack of cards, what is the probability of getting (a) a black card and (b) a king.

If P(A) = 0.6, P(B) = 0.5 and P(AUB) = 0.4, find P(A∩B). Where A and B are not mutually exclusive events.

Solve the following Linear Programming problem graphically:

Maximize Z = 30x + 50ySubject to constraints: x + y ≤ 30 x + 2y ≤ 40and x ≥ 0, y ≥ 0

Solve the following linear programming problem:

Minimize Z = 2x + 3ySubject to Constraint:5x + y ≥ 102x + 2y ≥ 12x + 4y ≥ 12x & y ≥ 0

a) From the given Pay-off table, give the decision according to

(i) Maximax approach (ii) Maximin approach (iii) Minimax Regret approach.

  (b) Two fair dice are rolled at the same time . What is the probability that the two faces turn up to show (i) a sum of 8 or 9 (iI) a sum less than 5 ? 

Solve the following problem graphically:

 Minimize the cost \( Z = \text{Rs. } 20x + \text{Rs. } 30y \)

Subject to constraints: \( 3x + 5y \ge 45 \)

                                   \( 2x + y \ge 20 \)

    and \( x, y \ge 0 \) non -negative condition

The manager of Flower shop promises its customers delivery within four hours on all flower orders. All flowers are purchased on the previous day and delivered to parker by 8.0 AM in the next morning. The daily demand for roses is as follows:

The manager purchase roses for Rs. 10 per dozen and sells them for Rs. 30. All unsold roses are donated to a local hospital. Construct the pay-off table. Also, find : EMV, EPPI and EVPI.

Find the value of determinant : 

Solve the following equations by using determinant or matrix method:

2x + 2y + z = 54x + 2y + 3z = 10x + 3y + 4z = 7

Find the value of determinant of following matrix:

The marks distribution of 100 students of a College is as follows:

 Determine the limits of marks of middle 805 students .

Solve the following system of linear equations by using determinant or matrix method: 2x - y + 2z = -1x - 2y + 3z = 44x + y + z = 4

Evaluate\( |A| = \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix} \)

Solve the following equations by using matrix or determent method

   3x + 2y + 5z = 10

   2x - 3y + 7z = 9

   x + y + z = 5

Find the value of determinant

Solve the following equations by using determinant or matrix method
5x + 3y + z = 16
2x + y + 3z = 19
x + 2y + 4z = 25

Find  7(A - B )  where A = 7    8           and  B =  6     3 

                                        9     10                          3      2

                                        2       5                          7     5 

Find 7(A+B) where A=

   and B = 

Find the transpose of matrix A where\( A = \begin{bmatrix} 1 & -2 \\ 4 & 3 \end{bmatrix} \)